MinT - Information on Result #1605711

Information on Result #1605711

Linear OOA(3¹⁶⁰, 9868, F₃, 4, 25) (dual of [(9868, 4), 39312, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁰, 9868, F₃, 2, 25) (dual of [(9868, 2), 19576, 26]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁶⁰, 19736, F₃, 25) (dual of [19736, 19576, 26]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3¹⁵⁶, 19731, F₃, 25) (dual of [19731, 19575, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(3¹⁴⁵, 19684, F₃, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(3¹⁰⁹, 19684, F₃, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(3¹¹, 47, F₃, 5) (dual of [47, 36, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [i]
  2. linear OA(3¹⁵⁶, 19732, F₃, 21) (dual of [19732, 19576, 22]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁵⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 34 158136 811949 666590 038157 562196 478848 675826 877445 383937 514472 917179 252699 [i]
  3. linear OA(3³, 4, F₃, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
    - dual of repetition code with length 4 [i]
    - oval in PG(2,Â 3) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁶⁰, 3289, F₃, 28, 25) (dual of [(3289, 28), 91932, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row